$$r+\frac{5}{r} = 0$$
Answer
$$ \begin{matrix}r_1 = \sqrt{ 5 } i & r_2 = -\sqrt{ 5 } i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} r+\frac{5}{r} &= 0&& \text{multiply ALL terms by } \color{blue}{ r }. \\[1 em]rr+r\cdot\frac{5}{r} &= r\cdot0&& \text{cancel out the denominators} \\[1 em]r^2+5 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+5 = 0 $ is a quadratic equation.
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